For practical purposes the Romans needed an accusation to charge Jesus in order to crucify him, because such a thing would become a matter of public record. In the second century AD Justin Martyr, while addressing the Emperor, Pius, mentioned that proof of what he said could be obtained from the Acts of Pilate, something that hardly could be so, if Pilate wasn’t required to record the reasons for the executions he commanded. Therefore, Pilate’s official verdict was: Jesus of Nazareth was the King of the Jews—a political crime, something for which he had earlier found him innocent. Nevertheless, he could hardly mention in a public record that he had executed Jesus for claiming to be the Son of God, a religious crime, according to the Jews (John 19:7, 13-16), but a matter of harmless superstition, according to Rome (cf. Acts 25:18-20).
Jesus was mocked, while he hung of the cross (Luke 23:34-38). Three days earlier he entered Jerusalem with praises coming from the crowds, and he was received by nearly everyone as the Messiah, King of the Jews (Luke 19:36-40; John 12:12-13). Nevertheless, as he left Jerusalem on that Passover, the day he was crucified, he was bloodied and beaten, rejected by the very people, who days before clung to him. A man followed him carrying the cross beam he would be nailed to, and the Romans went before him holding up the banner stating the accusation for which he would be slain – Jesus of Nazareth, King of the Jews (Luke 23:38).
While Jesus hung on the cross, the people, no longer shouting out alleluias, were simply gazing at him (Luke 23:35). Jesus was for them a sight to see. He healed all who came to him in the Temple over the past few days. He stood up to the Jewish authorities, who came against him, and sent them away, embarrassed and in fear of what he might do next. He even cast out all the business booths that traded within the Temple compound. They saw it all and enjoyed the spectacle. Now, they stood beholding Jesus, as he hung on the cross, perhaps half expecting a new miracle to applaud during their pilgrimage. No one, however, attempted to intervene or to object to what was taking place. They simply watched, as it all occurred before their eyes.
Ever since Jesus came to Jerusalem five days prior to this event, the chief priest and the other Jewish authorities sought to arrest him (Luke 19:47-48; 20:19; 22:2), but the people were very attentive to him, and the authorities feared to do anything to Jesus, believing their lives would be in danger, if they did. Now, however, the people seemed distant, so the Jewish authorities drew courage and mocked Jesus, as he hung on the cross, saying he couldn’t even save himself, how could he save others, but, if he should come down from the cross now, they would believe (Luke 23:35; Psalm 21:8; 22:6-8).
In light of all that was now being done to Jesus, the presence of the people at his execution seemed to be nothing more than a desire to witness the proceedings and not miss an unexpected occurrence. Perhaps, they thought Jesus ‘might’ save himself, after all, they were taught that the Messiah never dies (John 12:34), so, if this miracle worker really is the Messiah, maybe something unexpected would occur, and he will save himself. That would be something they simply wouldn’t want to miss, so they watched.
The Romans also joined in and mocked Jesus. Although they didn’t need any impetus to do such a thing, it was perhaps a rare sight to see one’s own countrymen turn against one of their victims. Therefore, they were also attentive to what the Jewish authorities were doing. The Roman soldiers also parted Jesus garments among themselves and cast lots for his festive garment (John 19:23-24), and offered the “King” a drink of sour wine (Luke 23:34, 36).
I don’t believe the Romans would have known enough to mock Jesus with the words: “save yourself” (Luke 23:37), if they hadn’t heard it from the Jews. After all, who would be able to save himself under such conditions? However, being informed of the Jewish doctrine that Christ continues forever (John 12:34) may have been a surprise they couldn’t resist to cast back in his teeth (cf. Matthew 27:44).
 Justin Martyr, First Apology chapter 35.